If the point P(x,y) is equidistant from the points A(5,1) and B(-1,5), prove that $3 x = 2 y$ .

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Solution

Let the point P(x,y) be equidistant from the points A(5,1) and B(-1,5). then,
$P A = P B$
$P A^{2} = P B^{2}$
$(x - 5)^{2} + (y - 1)^{2} = (x + 1)^{2} + (y - 5)^{2}$
$x^{2} + y^{2} - 10 x - 2 y + 26 = x^{2} + y^{2} + 2 x - 10 y + 26$
$12 x - 8 y = 0$
$12 x = 8 y$
$3 x = 2 y$

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Similar questions

(i) If the point P(2, 2) is equidistant from the points (a+b, b-a) and (a-b, a+b), prove that bx = ay.

(ii) If thedistances of P(x, y) from A(5, 1) and B (-1, 5) are equal then prove that 3x = 2y.

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